For the importance of deteriorating in units, this paper presents a Constraint
Deteriorating Probabilistic Periodic Review Inventory Model (CDPPRIM), a model
which is applicable under some assumptions: (1) the demand is a random variable
that follows Pareto distribution without lead time, (2) some costs are varying and
shortage is permitted, (3) the deterioration rate follows Gumbel distribution, and (4)
there is a constraint on varying deteriorating cost.
Here, the objective function under a constraint is imposed in crisp and fuzzy
environment. A Newton's method is used to solve the system of nonlinear
equations. The objective is to find the optimal values of four decision variables
(maximum inventory level, stock-out time, the deteriorating time, and review time),
which minimize the expected annual total cost under the assumptions. Finally, the
model is followed by an application.